Analogy Reasoning: Finding the Missing Number

The question presents a number analogy: 10 is related to 21 in the same way that 12 is related to the missing number.

We need to identify the pattern connecting the first pair of numbers (10 and 21) and apply it to the second number (12).

Step 1: Analyze the Relationship (10 : 21)

Let's examine possible mathematical operations:

• Multiplication and Addition: Multiply the first number by 2 and add 1.

  Calculation: $10 \times 2 + 1 = 20 + 1 = 21$. This matches the second number.

• Simple Addition: Add 11 to the first number.

  Calculation: $10 + 11 = 21$. This also matches.

The pattern $N \times 2 + 1$ is a common type in these analogies.

Step 2: Apply the Pattern (12 : ?)

Let's apply the identified pattern ($N \times 2 + 1$) to the second number, 12:

• Using the pattern $N \times 2 + 1$:

  Calculation: $12 \times 2 + 1 = 24 + 1 = 25$.

• Using the pattern $N + 11$:

  Calculation: $12 + 11 = 23$. This is not among the options.

The pattern $N \times 2 + 1$ yields 25, which is Option D.

Conclusion

The relationship is that the second number is obtained by multiplying the first number by 2 and adding 1. Applying this to 12 gives $12 \times 2 + 1 = 25$.